My favorites from Christie?
There are a few, but I would have to say And Then There Were None is the top one.
As for favorite detective, Poirot (after Mysterious Affair at Styles, of course, as that one I really disliked).
the other two you mention by name, I have not read many works featuring them, and Marple tends to come off as a boring detective, according to Gosho's profile of her in DC.